\chapter[Methods \\ \textnormal{\emph{Lectured in Michaelmas \oldstylenums{2021} by \textsc{Prof.\ E.\ P.\ Shellard}}}]{Methods}
\emph{\Large Lectured in Michaelmas \oldstylenums{2021} by \textsc{Prof.\ E.\ P.\ Shellard}}

In this course, we discuss various methods for solving differential equations.
Different forms of differential equations need different solution strategies, and we study a wide range of common types of differential equation.

A particularly powerful method for solving differential equations involves the use of Green's functions.
For example, physical systems can involve bodies spread over space with constant density.
Green's functions allow the equation to be solved for a point mass, and then integrated to find the solution for the larger body.

Fourier transforms are another way to solve differential equations.
Sometimes a differential equation is easier to solve after applying the Fourier transform to the relevant function, then the inverse Fourier transform recovers the solution to the original equation.

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